7 papers · 1 filter
On the optimal local well-posedness of the wave kinetic equation in
Ioakeim Ampatzoglou, Tristan Léger
In this paper, we give a unified treatment of the local well-posedness for the wave kinetic equation in almost critical weighted spaces with The proof…
Moment-preserving Young's inequality for the hard potential Boltzmann gain operator
Ioakeim Ampatzoglou, Tristan Léger, Tristan Léger
We prove a new moment-preserving Young's inequality for the gain operator of the Boltzmann equation with hard potentials, including the critical case of hard-spheres. Our approach…
On the ill-posedness of kinetic wave equations
Ioakeim Ampatzoglou, Tristan Léger
In this article we identify a sharp ill-posedness/well-posedness threshold for kinetic wave equations (KWE) derived from quasilinear Schrödinger models. We show well-posedness usi…
Derivation of the Higher Order Boltzmann Equation for Hard Spheres
Ioakeim Ampatzoglou, NataÅ¡a PavloviÄ, William Warner
In this paper we complete the program initiated by the first and second authors and rigorously derive a Boltzmann-type equation that incorporates higher order collisions among gas…
Global existence of strong solutions to the Inhomogeneous Kinetic Wave Equation
Ioakeim Ampatzoglou, Tristan Léger, Tristan Léger
In this paper we construct global dispersive solutions to the space inhomogeneous kinetic wave equation (KWE) which propagate moments and conserve mass, momentum and ene…
Inhomogeneous wave kinetic equation and its hierarchy in polynomially weighted spaces
Ioakeim Ampatzoglou, Joseph K. Miller, NataÅ¡a PavloviÄ +1
Inspired by ideas stemming from the analysis of the Boltzmann equation, in this paper we expand well-posedness theory of the spatially inhomogeneous 4-wave kinetic equation, and al…